So why is "ecclesiensis" singular when it is paired with "quinque" which is plural? The Latin name for Pecs is Quinque Ecclesiae. It has the same name in other languages to, e.g. Fünfkirchen in German. As far as I can discern, the two words should be taken together as one word. Hence you will see it elsewhere written, "Quinqueecclesiensis." This is then an adjective, meaning in English "of Quinque Ecclesiae" or rather "of Pecs."

Lbt's examples are good. It would be like saying, "the Parisian Diocese," rather than, "the Diocese of Paris."

You can see how it is practical here. There are other ways to make adjectives out of the word "ecclesia." "Ecclesiastical" for instance. But the -ensis suffix lets us know that its referring to a place. Otherwise, if we used a word like "ecclesiasticalis," it would easily give the impression that it is just a generic descriptor rather than the name of a particular place. When the adjective "Quinqueecclesiensis" is used, we know that this is the diocese of the place Quinque Ecclesia.

The reason that they use an adjective here instead of using the genitive case of the noun is just because that is the accepted style. For example, the official name for the Diocese of Paris in Latin is, I believe, Diocesis Parisiensis. Milan is Mediolanensis. Others might end in -ana instead of -ensis, but they are all adjectives, not nouns, as far as I know.

Also, it is not the case that -ensis is only used with non-native words. I don't know if there is any rule prohibiting -ensis from being used with a word. I did a quick Google and found this short article from a grammar textbook. You can see some various examples of words, such as "hortensis" (from "hortus," meaning "garden," definitely a native word).

It might be helpful to remember also that -ensis is the Latin form of the -ese suffix in English. The n disappears in other language due to nasalization. So Diocesis Mediolanensis is the Milanese Diocese.